Identify the Zeros and Their Multiplicities P(x)=5(x+1)^2(x-2)^3

$P (x) = 5 {(x + 1)}^{2} {(x - 2)}^{3}$

Set $5 {(x + 1)}^{2} {(x - 2)}^{3}$ equal to $0$ .

$5 {(x + 1)}^{2} {(x - 2)}^{3} = 0$

Solve for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

${(x + 1)}^{2} = 0$

${(x - 2)}^{3} = 0$

Set ${(x + 1)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x + 1)}^{2}$ equal to $0$ .

${(x + 1)}^{2} = 0$

Solve ${(x + 1)}^{2} = 0$ for $x$ .

Set the $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Set ${(x - 2)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(x - 2)}^{3}$ equal to $0$ .

${(x - 2)}^{3} = 0$

Solve ${(x - 2)}^{3} = 0$ for $x$ .

Set the $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $5 {(x + 1)}^{2} {(x - 2)}^{3} = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = - 1$ (Multiplicity of $2$ )

$x = 2$ (Multiplicity of $3$ )

$x = - 1$ (Multiplicity of $2$ )

$x = 2$ (Multiplicity of $3$ )

Identify the Zeros and Their Multiplicities P(x)=5(x+1)^2(x-2)^3

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